TOMS726
Orthogonal Polynomials and Quadrature Rules
TOMS726
is a FORTRAN77 library which
computes recursion relationships for various families of
orthogonal polynomials, as well as the abscissas and weights of
related quadrature rules;
the library is commonly called ORTHPOL, and is
by Walter Gautschi.
Languages:
TOMS726 is available in
a FORTRAN77 version and
a FORTRAN90 version.
Related Data and Programs:
TOMS655,
a FORTRAN77 library which
computes the weights for interpolatory quadrature rules.
TOMS793,
a FORTRAN77 library which
carries out Gauss quadrature for rational functions,
by Walter Gautschi;
this is ACM TOMS algorithm 793.
Reference:

William Cody, Kenneth Hillstrom,
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,
Mathematics of Computation,
Volume 21, Number 98, April 1967, pages 198203.

Walter Gautschi,
On Generating Orthogonal Polynomials,
SIAM Journal on Scientific and Statistical Computing,
Volume 3, Number 3, 1982, pages 289317.

Walter Gautschi,
Algorithm 726:
ORTHPOL  A Package of Routines for Generating Orthogonal
Polynomials and GaussType Quadrature Rules,
ACM Transactions on Mathematical Software,
Volume 20, Number 1, March 1994, pages 2162.
Source Code:
Examples and Tests:
List of Routines:

ALGA_R4 evaluates the logarithm of the gamma function.

ALGA_R8 evaluates the logarithm of the gamma function.

CHEB_R4 generates recursion coefficients ALPHA and BETA.

CHEB_R8 generates recursion coefficients ALPHA and BETA.

CHRI_R4 implements the Christoffel or generalized Christoffel theorem.

CHRI_R8 implements the Christoffel or generalized Christoffel theorem.

FEJER_R4 generates a Fejer quadrature rule.

FEJER_R8 generates a Fejer quadrature rule.

GAMMA_R4 evaluates the gamma function for real positive X.

GAMMA_R8 evaluates the gamma function for real positive argument.

GAUSS_R4 generates an Npoint Gaussian quadrature formula.

GAUSS_R8 generates an Npoint Gaussian quadrature formula.

GCHRI_R4 implements the generalized Christoffel theorem.

GCHRI_R8 implements the generalized Christoffel theorem.

KERN_R4 generates the kernels in the Gauss quadrature remainder term.

KERN_R8 generates the kernels in the Gauss quadrature remainder term.

KNUM_R4 integrates certain rational polynomials.

KNUM_R8 is a doubleprecision version of the routine KNUM_R4.

LANCZ_R4 applies Stieltjes's procedure, using the Lanczos method.

LANCZ_R8 is a doubleprecision version of the routine LANCZ_R4.

LOB_R4 generates a GaussLobatto quadrature rule.

LOB_R8 generates a GaussLobatto quadrature rule.

MCCHEB_R4 is a multiplecomponent discretized modified Chebyshev algorithm.

MCCHEB_R8 is a doubleprecision version of the routine MCCHEB_R4.

MCDIS_R4 is a multiplecomponent discretization procedure.

MCDIS_R8 is a doubleprecision version of the routine MCDIS_R4.

NU0HER estimates a starting index for recursion with the Hermite measure.

NU0JAC estimates a starting index for recursion with the Jacobi measure.

NU0LAG estimates a starting index for recursion with the Laguerre measure.

QGP_R4 is a generalpurpose discretization routine.

QGP_R8 is a doubleprecision version of the routine QGP_R4.

RADAU_R4 generates a GaussRadau quadrature formula.

RADAU_R8 generates a GaussRadau quadrature formula.

RECUR_R4 generates recursion coefficients for orthogonal polynomials.

RECUR_R8 is a doubleprecision version of the routine RECUR_R4.

STI_R4 applies Stieltjes's procedure.

STI_R8 is a doubleprecision version of the routine STI_R4.

SYMTR_R4 maps T in [1,1] to X in (oo,oo).

SYMTR_R8 maps T in [1,1] to X in (oo,oo).

T_FUNCTION solves Y = T * log ( T ) for T, given nonnegative Y.

TR_R4 maps T in [1,1] to X in [0,oo).

TR_R8 maps T in [1,1] to X in [0,oo).
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the FORTRAN77 source codes.
Last revised on 15 March 2008.